% --| other new definitions |-----------------------------------------



% --| Math |-------------------------------------------------------


% -- new commands --
\providecommand{\abs}[1]{\lvert#1\rvert}
\providecommand{\Abs}[1]{\left\lvert#1\right\rvert}
\providecommand{\norm}[1]{\left\Vert#1\right\Vert}
\providecommand{\Trace}[1]{\ensuremath{\Tr\{\,#1\,\}}} % Trace /Spur
%

% -- differentials --
\renewcommand{\d}{\partial\mspace{1mu}} % partial diff
\newcommand{\td}{\,\mathrm{d}}	% total diff
\newcommand{\ddt}[1]{\frac{\td #1}{\td t}}

% -- Abbrevitations --
\renewcommand{\Re}{\text{Re}}			% Real value
\renewcommand{\Im}{\text{Im}}			% Real value
\newcommand{\complex}{\mathbb{C}} % Complex
\newcommand{\real}{\mathbb{R}}    % Real
\renewcommand{\i}{\mathrm{i}}   
%\renewcommand{\L}{\mathcal{L}}
%\newcommand{\N}{\mathcal{N}}
%\newcommand{\R}{\mathcal{R}}
%\newcommand{\D}{\mathcal{D}}
%
\newcommand{\Ham}{\mathcal{H}}    
\newcommand{\Prob}{\mathscr{P}}   
\newcommand{\unity}{\mathds{1}}   
%
% -- New Operators --
\ifcsdef{DeclareMathOperator}{
  \DeclareMathOperator{\rot}{rot}
  \DeclareMathOperator{\grad}{grad}
  \DeclareMathOperator{\rect}{rect}
  \renewcommand{\div}{\text{div}\,}
  \DeclareMathOperator{\Tr}{Tr}
  \DeclareMathOperator{\const}{const}
  \DeclareMathOperator{\e}{e} 			% exponatial Function
}

% -- new symbols --
\newcommand{\laplace}{\Delta}
\newcommand{\dalembert}{\Box}

% -- new arrows --
\renewcommand{\leadsto}{\Longrightarrow}
\newcommand{\leftrightleadsto}{\Longleftrightarrow}


% -- other --
\newcommand{\com}[2]{\underbrace{#1}_{\textrm{\scriptsize #2}}}
\newcommand{\with}[1]{\stackrel{\ref{#1}}{\Longrightarrow}}

\newcommand{\variance}[1]{(\Delta{#1})^2}


% -- Physics --------------------------------
\newcommand\op[1]{{\hat{\mathrm{#1}}}}  % Operator
\newcommand\expect[1]{\ensuremath{\left\langle{#1}\right\rangle}} %
\newcommand{\mean}[1]{\ensuremath{\overline{#1}}} % mean value
\newcommand{\state}[1]{\ensuremath{\ket{#1}}}
%
\newcommand\commutator[2]{\ensuremath{\mathinner{%
    \mathopen[\,#1,#2\,\mathclose]}}}
\newcommand{\Commutator}[2]{\ensuremath{\left[\,#1,#2\,\right]}}
\newcommand{\bigcommutator}[2]{\ensuremath{\bigl[\,#1,#2\,\bigr]}}
\newcommand{\Bigcommutator}[2]{\ensuremath{\Bigl[\,#1,#2\,\Bigr]}}
%
\newcommand\poisson[2]{\mathinner{%
    \mathopen\{#1,#2\mathclose\}}}
%
